Paul's bomb doesn't have a tamper. You kind of need one; it needs to be big and heavy because otherwise the supercritical mass (whether it be plutonium or uranium) will dissipate too quickly, leading to a fizzle rather than a proper reaction. (A "pop" instead of a "boom".)
A typical warhead from an ICBM is made with depleted uranium. Uranium has excellent refractory properties, negating the need for a heat shield. The fission device fits inside this shell (called a "reentry vehicle" or RV) and the shell acts as a radiation shield, tamper, and neutron reflector.
It also weighs hundreds of pounds. And this is for a modern, boosted-fission weapon. Not exactly "man-portable" unless the man in question is lugging around a pallet jack with the weapon atop it.
For an implosion device, it takes 30 nanoseconds for the core to react, starting from the moment the explosives are detonated. This isn't long enough for the explosion shock wave to destroy the tamper or the rest of the bomb. By the time the shock wave reaches the tamper, the bomb has already finished detonating.
There's actually an ideal thickness for the tamper, too. Too thick and you waste energy vaporizing the tamper. Too thin and it doesn't confine the explosion or neutrons properly, and you lose energy that way. At the right thickness, you get the most power out of the reaction, which maximizes the yield of the bomb.
With stainless steel salad bowls providing the function of tamper and neutron reflector, Paul's device would have fizzled at best. In fact, it's more likely that the shoddy engineering of his device would have resulted in a "radiological release" rather than a nuclear detonation.
Why Do I Know This Stuff?
I've always been interested in physics. I knew the basics of nuclear bomb design when I was in grade school, believe it or not. The actual construction of a nuclear bomb is really not all that complex. The Manhattan Project employed all those scientists and engineers because it had never been done before--but they did all the hard work, and now making a nuke is just a matter of engineering.
The devil is in the details. While a nuke is not a complex device, it is still a precision device, especially in the case of an implosion device.
Over the years I've made a casual study of physics, from basic mechanics through the complex stuff. I don't know all the math, but I understand how things work and interact and can make up some reasonably plausible theories which more-or-less fit the framework of real physics, for the sake of my science fiction stories.
I've been snorting derisively at Hollywood's portrayal of nuclear weapons and nuclear power for a long time.
Atomic Train was written around the erroneous notion that an atomic bomb can go off if it's set on fire. Not true; in order to detonate an atom bomb everything must happen just right, in the proper order. And most modern plastic explosives will just burn if set afire. They do not use dynamite to detonate atom bombs; dynamite is too slow--and atom bombs are not black spheres with a long fuse and the word "BOMB" stenciled on them.
Atomic Twister was full of misconceptions about the design and operation of nuclear power plants. It was so wrong as to be ludicrous.
In China Syndrome, the movie focusses on the implied danger of nuclear power but it kind of glosses over the fact that the nuclear plant's safety systems function well enough to prevent a meltdown of the reactor core and a release of radiation--Jack Lemmon's stupidity notwithstanding. I mean, that's how the movie actually goes! The power plant doesn't melt down or release radiation. What "cautionary tale"?
What about the real world?
Nuclear power generation enjoys an enviable safety record. Commercial nuclear power plants in the United States have not killed very many people; may times fewer, in fact, than the number of people killed in coal mine accidents.
"Chernobyl"? Chernobyl killed 56 people; most of them were firemen who had been sent in to do something about the burning reactor core. 20 years later there has been no obvious increase in radiation-related diseases in the affected areas, either. In any event, the Chernobyl plant was built using an unsafe design and was deliberately operated in an unsafe fashion. No one builds graphite-moderated reactors any more, for the simple reason that graphite burns, and once it's on fire, it is notoriously difficult to extinguish.
There have been many accidents over the years, yes. People in the US have been killed by accidents involving research reactors. But the release of radioactivity into the environment has been avoided, and the people killed were people who were working with the reactors, not "innocent bystanders".
There have been "criticality accidents" in which fissile materials undergoing enrichment have concentrated enough to reach a critical mass and emit lots of radiation. Few such events have resulted in injury or loss of life, in the US, since the 1950s. (There were many in the former Soviet Union, as late as the 1980s.) The first few criticality events caused some fatalities. Most have not.
The biggest nuclear event prior to Chernobyl, in 1986, was Three Mile Island in the late 1970s. You could have camped out next to the containment vessel of the failing reactor for the duration of the entire event and you would have received a radiation dose slightly higher than the normal background radiation which is present all over the planet.
Among the people who lived in the area at the time of the event, cancer rates are slightly lower than the general population of the US. The slight depression in cancer rates is regarded as a statistical fluke and not significant; what is significant is that the cancer rates are essentially unchanged.
The plant released radioactive material, in the form of radioactive hydrogen. Being present at the top of the containment vessel at the time of that release would have subjected you to about 1,500 millirem of radiation. But, not to worry; if you ever have an angiogram, you can reasonably expect an exposure in the range of 15,000-25,000 millirem.
Have you ever released a helium balloon? Notice how quickly it rose into the air? A hydrogen molecule (H2) is one-half the weight of a helium atom. Being much lighter than air, hydrogen will tend to rise very rapidly; not much mixing will take place. And the most radioactive form of hydrogen--tritium--has a half-life of about seven years. About 1/8th of that tritium remains in the atmosphere as tritium right now; the rest has turned into lithium.
Discussions of the event at Three Mile Island seem to gloss over the fact that the safety systems of the plant prevented a significant release of radioactivity into the environment.
The unreasoning fear that people have for nuclear power mystifies me. It's not dangerous; certainly it's no more dangerous than boarding a jet airliner or driving to work. Yes, it can be hazardous; most useful tools are. But people who think nothing of using a bandsaw all day--a device which can lop off an arm without slowing down!--will fall over themselves to sign a petition against a proposed nuclear power plant.
Everything we do is dangerous, for crying out loud. You take a risk when you get into the shower. You take a risk when you cross a busy street. The important thing is to manage that risk, to take reasonable precautions in order to minimize the potential for disaster. You look both ways before crossing the street. You put down a non-skid mat before getting into the shower. These things minimize the risks but they do not eliminate it.